No-Idle Flow Shop Scheduling with Deteriorating Jobs and Common Due Date Under Dominating Machines

The phenomenon of deterioration effects can reduce production efficiency caused by extended start time or other factors. Based on it, this paper considers the scheduling situations of the common due date assignment in a no-idle flow shop scheduling environment. Under the given four dominating relationships (i.e., increasing, decreasing, increasing-decreasing and decreasing-increasing dominating machines, correspondingly expressed as idm, ddm, idm-ddm and ddm-idm) between machines, the objective functions are, respectively, to minimize (1) the weighted sum of common due date and total earliness; and (2) the weighted sum of common due date, total earliness and total penalty factors of tardy jobs. It is verified that these problems can be solved in polynomial time under four dominating relationships.